A gathering of $12$ people break into $3$ groups of $4$ to play $3$ different games : carrom

Question

A gathering of $12$ people break into $3$ groups of $4$ to play $3$ different games : carrom, UNO and bridge. Find the number of ways these $12$ people can be grouped.[1] Aaron and Sandy do not get along with each other and do not want to be in the same group. Find the number of ways these $12$ people can be grouped with this restriction.[3] Given that Aaron and Sandy are not in the same group, find the probability that a third person Billy is in the same group as Aaron.[3]

Accepted Answer

(a) $34650$ (b) $25200$ (c) $\dfrac{3}{10}$

2025 ACJC P2 Q7

2025 ACJC P2 Q7

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